School of Mathematics and Statistics - Theses
Now showing items 1-10 of 163
Transport equations and boundary conditions for oscillatory rarefied gas flows
A wide range of flow phenomena in everyday life can be modelled accurately using classical continuum theory: the Navier-Stokes equations with associated no-slip conditions. However, oscillatory flows generated by nanoscale ...
A combinatorial curvature flow for ideal triangulations
We investigate a combinatorial analogue of the Ricci curvature flow for 3-dimensional hyperbolic cone structures, obtained by gluing together hyperbolic ideal tetrahedra. Our aim is to find a hyperbolic structure for ...
Degree bounded geometric spanning trees with a bottleneck objective function
We introduce the geometric $\delta$-minimum bottleneck spanning tree problem ($\delta$-MBST), which is the problem of finding a spanning tree for a set of points in a geometric space (e.g., the Euclidean plane) such that ...
Promoting change in teacher practice through supported differentiation of instruction in mathematics
Differentiated instruction has been shown to be effective in improving student learning outcomes; however, the resulting work load can be difficult for teachers to manage. A teaching package known as the NRP (Number Resource ...
Topics in optimisation
This thesis addresses four problems in continuous and discrete optimisation. The first problem is about using column generation – an advanced technique in mixed integer programming – to design schedules for students in the ...
Spline techniques for incomplete and complex data
We consider incomplete data problems in two different complex data contexts: group testing data and functional data. In the group testing data context, we consider estimating the conditional prevalence of a disease from ...
Mechanistic and statistical models of skin disease transmission
At any one time, more than 160 million children worldwide are infected with skin sores. In remote Aboriginal Australian communities, prevalence is as high as 40%. Skin sores infected with Group A Streptococcus (GAS) can ...
An investigation of Australian rainfall using extreme value theory
In this thesis, we use extreme value theory to fit statistical models to observations of Australian daily rainfall extremes. We build upon the existing literature by challenging the basic assumptions of these models when ...
Selected problems in enumerative combinatorics: permutation classes, random walks and planar maps
In this thesis we consider a number of enumerative combinatorial problems. We solve the problems of enumerating Eulerian orientations by edges and quartic Eulerian orientations counted by vertices. We also find and prove ...
Unsteady motion of small particles in fluid: from autonomous propulsion to the interrogation of liquid-solid interfaces
Fluid flows at micro- and nanometre length scales are governed by physical processes that are quite different to their macroscale counterparts. When these flows interact with suspended solid particles, a rich array of ...